The White House did not specify if the meeting proposed by Trump would include just the member nations of the Gulf Cooperation Council - Kuwait, Qatar, Oman, Bahrain, the United Arab Emirates (UAE) and Saudi Arabia - or also other nations which have joined the diplomatic boycott of Qatar, Efe news reported.
"It is trying to describe this as an issue about the independence of their foreign policy, and it is not", Gargash said.
Riyadh and its allies accuse Qatar of supporting extremist groups and of serving the interests of regional arch-rival Iran, claims Doha has strongly rejected. Defence Secretary James Mattis spoke to his Qatari counterpart to express commitment to the region's security.
Turkey is a key ally of Qatar and is setting up a military base in the country which also hosts the largest U.S. air base in the Middle East.
Turkey is keen to support its close ally Qatar in a diplomatic crisis with Doha's Gulf neighbours, but has found itself with little room to manoeuvre given its ties with Riyadh, analysts say.
The UAE threatened to impose an economic embargo against Qatar while Bahrain said "any options" were on the table as the crisis in the Gulf showed no signs of abating on Thursday.
Since the diplomatic row erupted, slogans against and in support of Qatar have been among the top topics discussed on Twitter in Arabic, which is a hugely popular medium of expression in the Arab world, particularly in Saudi Arabia. While other airlines including Emirates, Etihad Airways, and Arabia have also announced similar moves.
"The United Arab Emirates' threat to jail anyone who objects to the government's policy on Qatar is completely inconsistent with the image of a forward-looking, cosmopolitan, global hub it seeks to cultivate", CPJ Middle East and North Africa Program Coordinator Sherif Mansour said from Washington, D.C.
Jordan also chose to revoke the license of Al Jazeera channel in the country, Minister of State for Media Affairs and the government spokesman Mohammad Momani said on Tuesday.
Qataris, meanwhile, were loading up on food supplies, fearing shortages.
Qatar's stock market may stabilise on Wednesday after two days of steep declines as some investors buy shares in companies with attractive valuations, but uncertainty over pressure on Qatar's banking sector could limit any rebound.
"It appears that President Trump is encouraging Saudi Arabia to put the screws into Qatar in order to force it into line with their hostile anti-Iranian Agenda along with the other GCC [Gulf Cooperation Council] states", he said.
Qatari Foreign Minister Sheikh Mohammed Abdulrahman al-Thani told the broadcaster that the Federal Bureau of Investigation has confirmed the hack and the planting of fake news.
"Saudi financing is still a major source of revenue for terrorist groups inside Syria, inside Iraq", then-Democratic presidential candidate Hillary Clinton said at a Council on Foreign Relations event in late 2015.
Kuwait's Emir Sheikh Sabah Al-Ahmad Al-Jaber al-Sabah flew to Saudi Arabia for talks with King Salman bin Abdulaziz, Saudi and Kuwaiti state media reported, but gave no details on the discussions.